Animation nodes color output - how to bake to keyframes as base color
You need to use the Set Keyframes node. Link to the docs.
It is designed to keyframe transforms (Loc, Rot, Scale), but you can keyframe other properties by choosing Custom in the first dropdown.
Click on the + icon to add a new field, and type color (implied object.color, that is to say the object viewport color) because that's the property you want to bake the keyframes to.
Check Enable to, well, enable the node's behavior.

Now if you play the animation, it will bake the keyframes to ALL frames.
How to restrict the baking to a certain frame range :
Add a Time Info node and a Compare boolean node.

Result :